Semilocal convergence analysis on the modifications for Chebyshev–Halley methods under generalized condition

In this paper, we consider the semilocal convergence for modifications of Chebyshev–Halley methods in Banach space. Compared with the results on super-Halley method studied in reference Gutiérrez and Hernández (1998)these modified methods need less computation of inversion, the R-order is improved, and the Lipschitz continuity of second derivative is also relaxed. We prove a theorem to show existence-uniqueness of solution. The R-order for these modified methods is analyzed under generalized condition.